Gain insights into coding matrix algebra operations in R and Rcpp. Explore matrix summation, multiplication, LU factorization, and eigendecomposition. Discover applications in machine learning, signal and image processing.

r.tar.gz

rcpp-and-armadillo

rcpp-eigen

rcpp-and-armadillo-spa

rcpp-and-armadillo-spa-copy

Matrix algebra is the foundation for machine learning, signal processing, image processing, and many other popular algorithms. It is very important that aspiring computer scientists get a solid understanding of the subject, and there’s no better way to achieve this than coding matrix algebra operations.

The course aims to teach you how to code matrix algebra operations in R, and with main C++ matrix algebra libraries: RcppArmadillo and RcppEigen. Moreover,  to clarify the matrix algebra operations, a simple algorithm is provided to understand the computing implications. The provided matrix algebra operations range from matrix summation and matrix multiplication to LU factorization and eigendecomposition.

The main course outcome is to develop hands-on experience via curated programs to perform the matrix algebra computation in the R and Rcpp ecosystem, also including the ability to develop algorithms for areas such as machine learning, image processing and signal processing.

Computing Matrix Algebra with R and Rcpp

# Inverse definition

An $(𝑛 \times 𝑛)$ square matrix $𝐴$ is called **invertible** (also nonsingular or nondegenerate) if there exists an $(𝑛 \times 𝑛)$ square matrix $𝐵$ such that:

$$ 𝐴𝐵 = 𝐵𝐴 = 𝐼_𝑛 $$

- Here, $𝐼_𝑛$ denotes the $(𝑛 \times 𝑛)$ #key# identity matrix: a diagonal matrix where each element in the diagonal is equal to one. #key# where we use ordinary matrix multiplication. 

- If the matrix is invertible, then the matrix $𝐵$ is uniquely determined by $𝐴$ and is called the **inverse of $𝐴$**, denoted by $𝐴^{−1}$.

Learn how to invert a matrix using R, Rcpp, Armadillo, and Eigen.

Introduction

Assignment Operator

Addition of Matrices

Scalar Multiplication of Matrices

Multiplication of Matrices

Transposition of Matrices

Determinant of a Matrix

Inverse of a Matrix

System of Linear Equations

LU Matrix Factorization

Cholesky Factorization

QR Matrix Factorization

Eigendecomposition

Wrapping It Up

Matrix Inversion

Inverse definition